In an optimization problem, a slack variable is a variable that is added to an inequality constraint to transform it to an equality. Introducing a slack variable replaces an inequality constraint with an equality constraint and a nonnegativity constraint.
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Some articles on slack variable:
... To each variable in the primal space corresponds an inequality to satisfy in the dual space, both indexed by output type ... To each inequality to satisfy in the primal space corresponds a variable in the dual space, both indexed by input type ... Since each inequality can be replaced by an equality and a slack variable, this means each primal variable corresponds to a dual slack variable, and each dual variable corresponds to a primal slack variable ...